Applying [1]} (\(\delta =1/4\) , \(\text{P}=1\)  therein), \(\mu \le 1/(4\text{R})\)  (cf. Lemma REF ), and noting that \(\mathbf {W}_{\text{j},\text{p}-1} = {\mathbf {W}_{\text{j},\text{p}-1}}_{\Omega _\text{j}}\) :
\(\Vert \mathbf {W}_{\text{i},\text{p}}\Vert _{\text{F}} \le \frac{1}{4} \Vert \mathbf {W}_{\text{i},\text{p}-1}\Vert _{\text{F}} + \frac{1}{4 \text{R}} \sum _{\text{j}\ne \text{i}} \Vert \mathbf {W}_{\text{j},\text{p}-1}\Vert _{\text{F}}, \quad 1 \le \text{i}\le \text{R}\) 
